easy Probability
A release-checked easy problem for training Coins, Expected Value/LOTUS, Dice, Conditional Expectation.
You have a fair standard 6-sided die and play the following game: You are paid the upface of every roll. If you roll an even value, the game is over. If you roll an odd value, you flip a fair coin. If it lands on tails, the game is over. If it lands on heads, you roll again and repeat the same coin flip process after your roll. Note that you do receive a payout that includes the roll the game ends. Find the expected payout from this game.
This Probability problem is tagged Coins, Expected Value/LOTUS, Dice, Conditional Expectation. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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